Slimani headed in Russia midfielder Aleksandr Golovin's corner in the 52nd minute, in a match where Monaco mostly dominated only to almost concede an injury-time equalizer. Moreno dropped former Spain midfielder Cesc Fàbregas and opted for a 4-3-3 with Stevan Jovetić supporting league top scorer Wissam Ben Yedder and Slimani.
Jovetić, twice, Ben Yedder and Golovin went close in a one-sided first half as Monaco snatched at chances on the way to securing a third straight win. Montpellier, strong at home but weak away, dropped to sixth spot.
Paris Saint-Germain will be without Neymar for the fourth straight game when it visits struggling Amiens on Saturday. The Brazil star is bidding to recover from a rib injury for Tuesday's match at Borussia Dortmund in the last 16 of the Champions League.
Second-placed Marseille, which trails PSG by 12 points, is at fourth-placed Lille on Sunday.
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